At the molecular level most of the new mutations occurring in a population are different from the alleles preexisting in the population and the classical concept of recurrent mutation is incorrect in the strict sense of the term. This new concept requires many new mathematical formulations of population dynamics of mutant genes, taking into account stochastic changes of gene or gamete frequencies. In the proposed study the following four problems will be studied from the standpoint of this idea. (1) Mathematical theories for the process of genetic differentiation of populations will be explored. The theories developed will be employed to study the factors which have caused racial differences in frequencies of normal and deleterious genes in man. (2) With the aim of clarifying the relatedness and evolution of human races, gene frequency data for a large number of protein loci will be analyzed by using genetic distance measure. The pattern of gene substitution in evolution will also be studied by looking at each enzyme locus separately in various organisms. (3) The mechanism of maintenance of deleterious mutations in human populations will be studied in terms of stochastic theory of gene frequency change. This study is intended to contribute to a better understanding of the mutational burden on the human society. (4) The theoretical basis of the use of marker genes in genetic counseling will be studied. Special attention will be given to the relationship between the utility of marker genes and gene frequencies.